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I am reading a paper which refers to a maximally skewed stable distribution $F(x;1,-1,\pi/2,0)$ . Is there an efficient way to sample from this distribution?

If $X$ has distribution $F(x;\alpha,\beta,\gamma,\delta)$, then when $\alpha=1$ its characteristic function $\phi(\theta) = \mathbb{E}(e^{-i\theta X})$, $\theta \in \mathbb{R}$ is given by

$$\phi(\theta) = e^{\gamma(-|\theta| - i\theta\beta (2/\pi)\log{|\theta|})+i\delta\theta}.$$

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there are the packages stabledist and FMStable that will do this for you.

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  • $\begingroup$ Thank you. I am not sure this package exactly covers the $\alpha=1$ case does it? It seems you would end up taking the limit as $\alpha \to 1$ which is a numerically unstable approach. $\endgroup$
    – Simd
    Commented May 20, 2014 at 12:09
  • $\begingroup$ FMStable allows you to set $1-\alpha$ explicitly and claims high accuracy. $\endgroup$
    – Carlo Beenakker
    Commented May 20, 2014 at 12:20
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Table 1 of http://arxiv.org/abs/0908.3961v2 contains an explicit algorithm for this.

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